A Concrete Approach to Abstract Algebra: From the Integers to the Insolvability of the Quintic
Autor Jeffrey Bergenen Limba Engleză Paperback – 5 mar 2010
It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study.
This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus.
- Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra
- Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems
- Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms
- Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices
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Specificații
ISBN-13: 9780123749413
ISBN-10: 0123749417
Pagini: 720
Dimensiuni: 193 x 236 x 36 mm
Greutate: 1.38 kg
Editura: ELSEVIER SCIENCE
ISBN-10: 0123749417
Pagini: 720
Dimensiuni: 193 x 236 x 36 mm
Greutate: 1.38 kg
Editura: ELSEVIER SCIENCE
Public țintă
Advanced undergraduate and graduate students taking a course in abstract algebra.Cuprins
Introduction;
What
This
Book
Is
about
and
Who
This
Book
Is
for;
Proof
and
Intuition;
The
Integers;
Rational
Numbers
and
the
Real
Numbers;
The
Complex
Numbers;
The
fundamental
Theorem
of
Algebra;
The
Integers
Modulo
n;
Group
Theory;
Polynomials
over
the
Integers
and
Rationals;
Roots
of
Polynomials
of
Degree
Less
than
5;
Rational
Values
of
Trigonometric
Functions;
Polynomials
over
Arbitrary
Fields;
Difference
Functions
and
Partial
Fractions;
An
Introduction
to
Linear
Algebra
and
Vector
Spaces;
Degrees
and
Galois
Groups
of
Field
Extensions;
Geometric
Constructions;
The
Insolvability
of
the
Quintic;
Bibliography;
Index